What is expand (2x+e^x)(x^2-e^x) ?

The solution to expand (2x+e^x)(x^2-e^x) is 2x^3-2e^xx+e^xx^2-e^{2x}

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expand (2x+e^x)(x^2-e^x)

expand

(2 x + e^{x}) (x^{2} - e^{x})

2 x^{3} - 2 e^{x} x + e^{x} x^{2} - e^{2 x}

Solution steps

(2 x + e^{x}) (x^{2} - e^{x})

Apply FOIL method:

(a + b) (c + d) = a c + a d + b c + b d

a = 2 x, b = e^{x}, c = x^{2}, d = - e^{x}

= 2 x x^{2} + 2 x (- e^{x}) + e^{x} x^{2} + e^{x} (- e^{x})

Apply minus-plus rules

+ (- a) = - a

= 2 x^{2} x - 2 e^{x} x + e^{x} x^{2} - e^{x} e^{x}

Simplify

2 x^{2} x - 2 e^{x} x + e^{x} x^{2} - e^{x} e^{x} : 2 x^{3} - 2 e^{x} x + e^{x} x^{2} - e^{2 x}

= 2 x^{3} - 2 e^{x} x + e^{x} x^{2} - e^{2 x}

\frac{7 ( e - 1 )}{1 - e}

\frac{( 2 + 5 i ) ^{7}}{( - 5 + 2 i ) ^{5}}

\frac{r ( r - x ^{2} r l c ) - i x l}{( r - x ^{2} r l c ) + x ^{2} l ^{2}}

(e^{i θ} - e^{- i θ})^{6}

- \frac{2 ( x - b )}{3}

What is expand (2x+e^x)(x^2-e^x) ?
The solution to expand (2x+e^x)(x^2-e^x) is 2x^3-2e^xx+e^xx^2-e^{2x}